Appendix: Applying Epidemic Models to Economic Narratives
1. Miller (2012) derives this equation from a stochastic model based on Poisson processes and
generalizing to variants of the Kermack-McKendrick model.
2. See Carvalho and Gonçalves, 2016, https://arxiv.org/pdf/1609.09313.pdf.
3. The common rate equations in chemistry resemble closely the three-equation system shown here, but
with SI in the first two equations replaced with just S. https://bio.libretexts.org/TextMaps/Map%3A
_Biochemistry_Online_(Jakubowski)/06%3A_TRANSPORT_AND_KINETICS/B._Kinetics_of_Simple
_and_Enzyme-Catalyzed_Reactions/B2._Multi-Step_Reactions.
Here S, I, and R are three chemicals together, and the model is, for example, applied to radioactive decay
of three elements together, where S, I, and R are the quantities of the elements, where I refers to the
intermediate element, and R the last element, which is stable. There are the same two parameters c and r,
and plots of S, I, and R may look similar to those here, with a hump-shaped pattern for I, and there are both
fast and slow reactions depending on c and r. But in that consecutive chemical reactions model, the size of
the epidemic is always 100%. More similar models in chemistry involve reactions that require the pairing of
chemicals in a solution. https://www.chemguide.co.uk/physical/basicrates/arrhenius.html.
4. The SIRS model is the same as the SIR model above except that a term +sR is added to the right-hand
side of the first equation and −sR to the right-hand side of the third equation, where s > 0 is a re-
susceptibility rate. In this model the infectives’ path may, depending on parameters, look similar to that in
Figure A.1 but approaching a nonzero horizontal asymptote as time increases: the infectives never
effectively disappear, and the disease becomes endemic. See Breda et al., 2012.
5. Grais et al., 2004.
6. Legrand et al., 2007.
7. Long et al., 2008.
8. JSTOR catalogs over nine million scholarly articles and books in all fields, and 7% of these are in
business or economics, but 25% of the articles with “ARIMA,” “ARMA,” or “autoregressive” are in
business or economics.
9. Moving average models are sometimes justified by reference to the Wold decomposition theorem
(1954), which shows that any covariance stationary stochastic process can be modeled as a moving average
of noise terms plus a deterministic component. But there is no justification for assuming that simple variants
of ARIMA models are so general. We may be better able to do economic forecasting in some cases if we
represent these error terms or driving variables as the result of co-epidemics of narratives about which we
have some information.
10. See Nsoesie et al., 2013.
11. Nathanson and Martin, 1979.
12. Bailey et al., 2016.
13. Surveyed in Lamberson, 2016.
14. See Banerjee, 1992; Bikhchandani et al., 1992.
15. Goel et al., 2016.
16. Katz and Lazarsfeld, 1955, pp. 44–45.
17. Herr et al., 1991.
18. Bauckhage, 2011.
19. Shiller and Pound, 1989, p. 54. The words in square brackets were omitted from the version of this
question given to individual investors.
20. http://knowledge.wharton.upenn.edu/article/is-this-the-end-of-money/.
21. Rand and Wilson (1991), Zeng et al. (2005), Zheng et al. (2015), and Olsen et al. (1988) claim that a
chaotic form of the SEIR model fits data on epidemics of measles, mumps, and rubella.
22. The basic idea of an information cascade was developed by Banerjee (1992) and Bikhchandani et al.

(1992), carried further by Vives (1996) and Banerjee and Fudenberg (2004).
23. Akerlof and Yellen, 1985.
24. Restaurant choice is the featured example in Banerjee, 1992.
25. Banerjee and Fudenberg (2004) address the question, from game theory, when thoroughly rational
actors may form a consensus on false information.